Measurements of small forces, in the nanonewton and piconewton range, have become important in recent years due to the widespread use of the Atomic Force Microscope (AFM) and associated instruments. There is a need to measure such small forces accurately, for example, protein-protein interactions or materials properties via the small force applied to an indenting tip.
The quantification of interaction forces is much more problematic. Force on the tip is inferred from the deflection of the cantilever, using an assumed value for the cantilever spring constant. The accuracy to which the spring constant is known is the limiting factor in the accuracy of a force measurement. Many methods have been proposed for calibrating the stiffness of an AFM probe, but none are traceable, and typical accuracy is only about 20-30%.
Reference artifacts for dimensional calibration of AFM have been available from many sources for ten years or more, but calibration of the force constant of AFM cantilevers is more troublesome. Uncalibrated cantilevers lead to very large errors in the measurement of nanonewton forces, such as in direct experiments to break individual covalent bonds by AFM, or the measurement of protein interaction forces. Commercial reference artifacts are available, but offer no traceability to the SI measurement system. This is important because there are two important methods of measuring nanoscale forces, AFM and optical tweezers. AFM is most conveniently calibrated using reference cantilevers, whereas optical tweezer forces are estimated based on the rate of change of photon momentum. Both methods are used, for example, in measuring bond-breaking forces. They must both have a common force scale, or burgeoning work in both areas will be difficult to build-upon. What is more, a traceable calibration method is now timely.
AFMs measure topography accurately, and are calibrated for this purpose quite easily using step-height standards. Some AFM instruments even incorporate laser interferometry to make traceable height measurements. However accuracy is rarely mentioned for AFM force measurements. There is an increasing need for the accurate measurement of small lateral forces by AFM, in the mechanical analysis of contamination on semiconductor surfaces, polymer blends, functional thin films, recording media and measuring adhesion of nanoparticulates at surfaces. The lateral force signal is useful for identifying surface composition where the materials are relatively flat but have significantly different friction characteristics. When combined with the use of chemically functionalised AFM tips, lateral force imaging can reveal contrast between different surface species where none can be seen in any other scanned probe mode. Many existing and future applications use the lateral force signal only to provide image contrast, but in many other applications the quantitative comparison of lateral force measurements is essential. This has been difficult so far, due to the wide range of torsional constants seen in even supposedly similar cantilevers. Cantilever coatings, to improve reflectivity, or chemically functionalise the tip, can have a significant effect on spring and torsional constants that are difficult to model. A calibration method is required.
A wide variety of methods have been used to calibrate normal spring constant, including thermal vibrations, reference cantilevers of measured dimensions, and radiation pressure. Commonly assigned co-pending patent application No. PCT/GB2004/002134, which is herein incorporated by reference discloses a MEMS device designed for the calibration of normal forces in AFMs, allowing piconewton and nanonewton force measurements to be made traceable to the SI system. However, calibration of lateral forces is more of a problem. Thermal vibrations can be useful, but there are fewer other options. Many of the methods that have been tried for the purpose of normal force calibration have extensions to allow the calibration of lateral forces, but some have no obvious method of being extended in this way, and are likely to be limited to the calibration of normal forces only. Those existing methods able to measure the torsional constant typically require accurate dimensional measurements (e.g. in an SEM) or high frequency power spectrum measurement that is beyond the bandwidth of the signal amplifiers supplied as part of the AFM electronics. In other words, these methods require additional facilities the AFM user may not have access to, and even if available, requires special training to achieve the accuracy needed.